At what depth in the lake will a bubble of air have one half the volume it will have on reaching the

Question

At what depth in the lake will a bubble of air have one half the volume it will have on reaching the surface. (The height of the barometer at that time is 76 cm mercury)\

Professor PC Thomas Classes · Answer

Let $h$ be the depth of the lake. Atmospheric pressure $=76 \mathrm{~cm}$ of Hg $$ =76 	imes 13.6 \mathrm{~cm} 	ext { of water } $$ Refer to above figure\ $\mathrm{P}_{1}=(76 	imes 13.6)+\mathrm{h} ; \quad \mathrm{V}_{1}=\mathrm{V}$\ $\mathrm{P}_{2}=76 	imes 13.6 ; \quad \mathrm{V}_{2}=2 \mathrm{~V}$\ Apply $\mathrm{P}_{1} \mathrm{~V}_{1}=\mathrm{P}_{2} \mathrm{~V}_{2}$ and get the volume of h\